{"paper":{"title":"Zero-sum flows for Steiner triple systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.C. Burgess, E. Mendelsohn, P. Danziger, S. Akbari","submitted_at":"2015-02-13T19:31:51Z","abstract_excerpt":"Given a $2$-$(v,k,\\lambda)$ design, $\\cal{S}=(X,\\cal{B})$, a {\\it zero-sum $n$-flow} of $\\cal{S}$ is a map $f: \\cal{B} \\longrightarrow \\{\\pm 1, \\ldots ,\\pm (n-1)\\}$ such that for any point $x\\in X$, the sum of $f$ around all the blocks incident with $x$ is zero. It has been conjectured that every Steiner triple system, STS$(v)$, on $v$ points $(v>7)$ admits a zero-sum $3$-flow. We show that for every pair $(v,\\lambda)$, for which a triple system, TS$(v,\\lambda)$ exists, there exists one which has a zero-sum $3$-flow, except when $(v,\\lambda)\\in\\{(3,1), (4,2), (6,2), (7,1)\\}$ and except possibl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04096","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}